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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

The Buzzard-Diamond-Jarvis conjecture for unitary groups


Authors: Toby Gee, Tong Liu and David Savitt
Journal: J. Amer. Math. Soc. 27 (2014), 389-435
MSC (2010): Primary 11F33, 11F80
Published electronically: July 3, 2013
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Abstract: Let $ p>2$ be prime. We prove the weight part of Serre's conjecture for rank two unitary groups for mod $ p$ representations in the unramified case (that is, the Buzzard-Diamond-Jarvis conjecture for unitary groups), by proving that any Serre weight which occurs is a predicted weight. Our methods are purely local, using the theory of $ (\varphi ,\hat {G})$-modules to determine the possible reductions of certain two-dimensional crystalline representations.


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Additional Information

Toby Gee
Affiliation: Department of Mathematics, Imperial College London, London, SW7 2AZ United Kingdom
Email: toby.gee@imperial.ac.uk

Tong Liu
Affiliation: Department of Mathematics, Purdue University, 150 N.\ University Street, West Lafayette, Indiana 47907
Email: tongliu@math.purdue.edu

David Savitt
Affiliation: Department of Mathematics, University of Arizona, 617 N.\ Santa Rita Avenue, Tucson, Arizona 85721-0089
Email: savitt@math.arizona.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-2013-00775-4
PII: S 0894-0347(2013)00775-4
Received by editor(s): July 5, 2012
Received by editor(s) in revised form: May 15, 2013
Published electronically: July 3, 2013
Additional Notes: The second author was partially supported by NSF grant DMS-0901360.
The third author was partially supported by NSF grant DMS-0901049 and NSF CAREER grant DMS-1054032.
Article copyright: © Copyright 2013 American Mathematical Society